Arguments and Quarrels

In everyday life, an argument and a quarrel are the same thing: a disagreement unfolding, typically very heated and tense, perhaps with lots of insults and name-calling.

But in the world of logic, an argument is not the same thing as these low-level quarrels. A logical argument consists of

1.  premises that are assumed to be true
2. logical rules that unfold and transform these premises
3. conclusions to arrive at, as a result of these transformations

In real life, such as in debates and essays, we typically go in the order of 3, 1, 2, to make logical arguments, but the basic elements remain the same no matter what order or context we present them. And oftentimes, there isn’t even anyone to disagree with in a logical argument because they are typically in written form, but it’s almost always better to make logical arguments and discussions with friends and classmates.

Logical System

A logical system is a combination of 1. assumptions, 2. syntax rules, 3. inference rules, and 4. the true conclusions as a result of these. That’s a lot to unpack, but let’s break it down one by one.

You might know some saying about how assumptions make bad people out of you and me, but acknowledging the existence of assumptions and of your own assumptions is important in being logical. Any idea of truth in a logical system has to have a starting point, so assumptions are a necessary evil to start moving forward with logical truth. But if at any point, we logically make a false conclusion, then our assumptions must have been wrong, and we must abandon them.

Syntax will be explained more in-depth in the next section, but it’s about “even making sense.” If I were to say “Gets gambles man live,” that probably wouldn’t make any sense to an English speaker, and we can’t even begin to discuss whether it’s true or false.

Inference rules tell us how to combine and transform old truths into new truths. We’ll get deeper into these in later articles. Finally, conclusions are these new truths that we can reach.

Syntax and Semantics
Syntax is about following the rules and having the correct form of any logical system. We can think about it like “the rules of the game.” For example, if the NBA decided one day to abandon all the rules of basketball, it would be hard to call the game “basketball” anymore. Similarly, by having syntactic errors in a logical argument, it would be harder to call any conclusions you make “logical.” 

Essentially, syntax is being “grammatically correct” within some logical system.
Semantics is the concept of actual substance and meaning. Syntax was about having the correct skeleton, and semantics is about filling it up with the meat, muscles, fat, and all. Semantics is about actually understanding and playing the game. I could learn every single letter of the NBA rulebook forwards and backwards, but that doesn’t suddenly make me LeBron James. I need to both understand the rules and play the game to win. 

Likewise, we need to be both syntactically and semantically correct to discover logical truth.

Syntax without Semantics

“Colorless green ideas sleep furiously,” Noam Chomsky once wrote, in explaining semantically meaningless, but syntactically correct, sentences. For real, what does it mean to be both “colorless” and “green”? What does it even mean for an idea to be either “colorless” or “green”? How do ideas “sleep”? How can something sleep furiously?

Chomsky’s point was that even though this is a grammatically correct sentence, it is basically completely meaningless. Semantics is generally more complicated than just the syntax of a system. A great architectural design principle to sum this up is that “form follows function”: form and rules are subservient to meaning and purpose.

Homework:

What are some examples of logical systems? What are some of their assumptions and conclusions? (Examples include physics and biology. Physics assumes everything follows physical laws, like conservation of momentum and has made conclusions in the form of predictions of, for example, the orbits of the planets. Biology assumes life is an inherently chemical process and has made conclusions such as Darwinian evolutionary theory.)